IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v115y2005i5p781-796.html
   My bibliography  Save this article

A two-species competition model on

Author

Listed:
  • Kordzakhia, George
  • Lalley, Steven P.

Abstract

We consider a two-type stochastic competition model on the integer lattice . The model describes the space evolution of two "species" competing for territory along their boundaries. Each site of the space may contain only one representative (also referred to as a particle) of either type. The spread mechanism for both species is the same: each particle produces offspring independently of other particles and can place them only at the neighboring sites that are either unoccupied, or occupied by particles of the opposite type. In the second case, the old particle is killed by the newborn. The rate of birth for each particle is equal to the number of neighboring sites available for expansion. The main problem we address concerns the possibility of the long-term coexistence of the two species. We have shown that if we start the process with finitely many representatives of each type, then, under the assumption that the limit set in the corresponding first passage percolation model is uniformly curved, there is positive probability of coexistence.

Suggested Citation

  • Kordzakhia, George & Lalley, Steven P., 2005. "A two-species competition model on," Stochastic Processes and their Applications, Elsevier, vol. 115(5), pages 781-796, May.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:5:p:781-796
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(04)00188-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kortchemski, Igor, 2015. "A predator–prey SIR type dynamics on large complete graphs with three phase transitions," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 886-917.
    2. Igor Kortchemski, 2016. "Predator–Prey Dynamics on Infinite Trees: A Branching Random Walk Approach," Journal of Theoretical Probability, Springer, vol. 29(3), pages 1027-1046, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:115:y:2005:i:5:p:781-796. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.